Plain Sedimentation
232. Theory of Sedimentation.—Sedimentation takes place in sewage because some particles of suspended matter have a greater specific gravity than that of water. All particles do not settle at the same rate. Since the weights of particles vary as the cubes of their diameters, whereas the surface areas (upon which the action of the water takes place) vary only as the squares of the diameters, the amount of the skin friction on small particles is proportionally greater than that on large particles, because of the relatively greater surface area compared to their weight. As a result the smaller particles settle more slowly. The velocity of sedimentation of large particles has been found to vary about as the diameter and of small particles as the square root of the diameter. The change takes place at a size of about 0.01 mm.
Sedimentation is accomplished by so retarding the velocity of flow of a liquid that the settling particles will be given the opportunity to settle out. The slowing down of the velocity is accomplished by passing the sewage through a chamber of greater cross-sectional area than the conduit from which it came. The time that the sewage is in this chamber is called the period of retention. Although the shape of a basin, the arrangement of the baffles and other details have a marked effect on the results of sedimentation, the controlling factors are the period of retention and the velocity of flow. Another factor affecting the efficiency of the process is the quality of the sewage. Usually the greater the amount of sediment in the sewage the greater the per cent of suspended matter removed. A method for the determination of the proper period of sedimentation has been developed by Hazen in Transactions of the American Society of Civil Engineers, Volume 53, 1904, page 45. The results of his studies are summarized in Fig. 154 which shows the per cent of sediment remaining in a treated water after a certain period of retention. This period of retention is expressed in terms of the hydraulic coefficient[[143]] of the smallest size particle to be removed. Table 77 shows the hydraulic coefficients of various particles. In Fig. 154 a represents the period of retention and t the time that it would take a particle to fall to the bottom of the basin. The different lines of the diagram represent the results to be expected by various arrangements of settling basins. The meaning of these lines is given in Table 78.
| TABLE 77 | |
|---|---|
| Hydraulic Values of Settling Particles in Millimeters per Second | |
| Diameter in mm. | Hydraulic Value |
| 1.00 | 100 |
| 0.80 | 83 |
| 0.60 | 63 |
| 0.50 | 53 |
| 0.40 | 42 |
| 0.30 | 32 |
| 0.20 | 21 |
| 0.15 | 15 |
| 0.10 | 8 |
| 0.08 | 6 |
| 0.06 | 3.8 |
| 0.05 | 2.9 |
| 0.04 | 2.1 |
| 0.03 | 1.3 |
| 0.02 | 0.62 |
| 0.015 | 0.35 |
| 0.010 | 0.154 |
| 0.008 | 0.098 |
| 0.006 | 0.055 |
| 0.005 | 0.0385 |
| 0.004 | 0.0247 |
| 0.003 | 0.0138 |
| 0.002 | 0.0062 |
| 0.0015 | 0.0035 |
| 0.001 | 0.00154 |
| 0.0001 | 0.0000154 |
An example will be given to illustrate the method of using the diagram and tables to determine the size of a sedimentation basin to perform certain required work.
Let it be required to determine the period of retention in a continuously operated sedimentation basin with good baffling, corresponding to two properly baffled sedimentation basins in series. The basins are to remove 60 per cent of the finest particles which are to have a size of .01 mm. The quantity to be treated daily is 3,000,000 gallons.
1st. Entering Table 77, we find that the hydraulic value of the finest particles is .154 mm. per second.
2d. Since we wish to remove 60 per cent of the finest particles, 40 per cent will remain. Since Fig. 154 shows the per cent remaining after the time a
t we enter Fig. 154 at 40 per cent on the ordinates and run horizontally until we encounter Line 4 corresponding to good baffling in Table 78. We then run down vertically from this intersection and find that the ratio of a
t is 1.0.
Then a equals t, which means that the period of retention should equal the time that it takes a particle 0.01 mm. in diameter to drop from the top to the bottom of the basin. Since this depends on the depth of the basin it is necessary to determine the depth before the other dimensions of the basin can be fixed.
Although this method is seldom used in practice for the final design of a sedimentation basin, it is a guide to judgment and can be used to supplement the data obtained from tests.
Fig. 154.—Hazen’s Diagram, Showing the Relation between the Time of Settling and the Period of Retention in Various Types of Sedimentation Basins.
Trans. Am. Society Civil Engineers, Vol. 53, 1904, p. 45.
| TABLE 78 | ||||
|---|---|---|---|---|
| Comparison of Different Arrangements of Settling Basins | ||||
| (From Hazen) | ||||
| Description of Basins | Line in Fig. 154 | Values of a t. | ||
| Per Cent of Matter Removed | ||||
| 50 | 74 | 87.5 | ||
| Theoretical maximum. Cannot be reached. | A | 0.50 | 0.75 | 0.875 |
| Surface skimming. Rockner Roth system. | B | 0.54 | 0.98 | 1.37 |
| Intermittent basins, reckoned on time of service only. | C | 0.63 | 1.26 | 1.89 |
| Continuous basin. Theoretical limit. | D | 0.69 | 1.38 | 2.08 |
| Close approximation to the above. | 16 | 0.71 | 1.45 | 2.23 |
| Very well baffled basin. | 8 | 0.73 | 1.62 | 2.37 |
| Good baffling. | 4 | 0.76 | 1.66 | 2.75 |
| Two basins, tandem. | 2 | 0.82 | 2.00 | 3.70 |
| One long basin, well controlled. | 1.5 | 0.90 | 2.34 | 4.50 |
| Intermittent basin in service half time. | E | 1.26 | 2.50 | 3.80 |
| One basin, continuous. | 1 | 1.0 | 3.00 | 7.00 |
The design of sedimentation basins should be based on experimental observations made upon the quantity of sediment removed at certain rates of flow and periods of retention in different types of basins. Hazen’s mathematical analysis is serviceable in making preliminary estimates and in checking the results. The shape of the tank, period of retention and rate of flow producing the most desirable results should be duplicated with the expectation of obtaining similar results or results but slightly modified from those obtained in the tests. This is the most satisfactory method of determining the proper period of retention.
233. Types of Sedimentation Basins.—A sedimentation basin is a tank for the removal of suspended matter either by quiescent settlement or by continuous flow at such a velocity and time of retention as to allow deposition of suspended matter.[[144]] The difference between sedimentation tanks and other forms of tank treatment is that no chemical or biological action is depended on for the successful operation of the tank. Sedimentation tanks may be divided into two classes, grit chambers and plain sedimentation basins.
A grit chamber is a chamber or enlarged channel in which the velocity of flow is so controlled that only heavy solids, such as grit and sand, are deposited while the lighter organic solids are carried forward in suspension. If the velocity of flow is more than about one foot per second, the tank is a grit chamber and below this velocity it is a plain sedimentation basin.
There are six general types of plain sedimentation basins:
1st. Rectangular flat-bottom tanks operated on the continuous-flow principle.
2nd. Rectangular flat-bottom tanks operated on the fill and draw principle.
3rd. Rectangular or circular hopper-bottom tanks operated on the continuous-flow principle, with horizontal flow.
4th. Rectangular or circular hopper-bottom tanks operated on the fill and draw principle, with horizontal flow.
5th. Rectangular or circular hopper-bottom tanks operated on the continuous-flow principle with vertical flow.
6th. Circular hopper-bottom tanks operated on the continuous-flow principle with radial flow.
| TABLE 79 | |||||
|---|---|---|---|---|---|
| Critical Velocities for the Transportation of Debris | |||||
| Sedimentation will not Occur at Higher Velocities | |||||
| Diameter of Particle in Millimeters | Critical Velocity, Feet per Second. | Size of Screen or Number of Meshes per Inch | |||
| Specific Gravity | |||||
| 1.5 | 2.0 | 3.0 | 5.0 | ||
| 0.010 | 0.13 | 0.20 | 0.22 | 0.28 | |
| 0.050 | 0.23 | 0.34 | 0.39 | 0.50 | More than 200 |
| 0.100 | 0.30 | 0.42 | 0.50 | 0.65 | More than 150 |
| 0.500 | 0.55 | 0.73 | 0.91 | 1.15 | More than 28 |
| 1.0 | 0.71 | 0.92 | 1.18 | 1.50 | More than 14 |
| 1.25 | 0.77 | 1.00 | 1.30 | 1.60 | |
| 2.0 | 0.92 | 1.20 | 1.50 | 1.90 | More than 10 |
| 5.0 | 1.30 | 1.70 | 2.20 | 2.60 | More than 4 |
| 10 | 1.70 | 2.20 | 2.8 | 3.4 | |
| Diameter in Millimeters for a Velocity of 1 Foot per Second | |||||
| 2.5 | 1.25 | 0.65 | 0.32 | ||
234. Limiting Velocities.—Sand, clay, bits of metal and other particles of mineral matter will commence to deposit in appreciable quantities when the velocity of flow falls below 3 feet per second. The amount deposited will increase as the velocity decreases. In Table 79 are given the approximate horizontal velocities at which certain size particles of mineral matter will deposit. At a velocity of about one foot per second organic matter will commence to deposit. It will be noticed by interpolation in Table 79,[[145]] that particles with the same specific gravity as sand (2.6), larger than one mm. in diameter will deposit at a velocity of about one foot per second or less, and that smaller and lighter particles will not deposit at velocity of one foot per second or greater. It will also be noticed that a velocity of one foot per minute is sufficiently slow to permit the deposit of the smallest and lightest particles. For this reason velocities of 1 or 2 or even 3 feet per second have been adopted as the velocities in grit chambers and velocities less than 1 foot per minute in plain sedimentation basins.
235. Quantity and Character of Grit.—The amount of material deposited in grit chambers varies approximately between 0.10 and 0.50 cubic yard per million gallons. It is to be noted that grit chambers are used only for combined and storm sewage and for certain industrial wastes. They are unnecessary for ordinary domestic sewage. The material deposited in grit chambers operating with a velocity greater than one foot per second is non-putrescible, inorganic, and inoffensive. It can be used for filling, for making paths and roadways, or as a filtering material for sludge drying beds. An analysis of a typical grit chamber sludge is shown in Table 80.
| TABLE 80 | |||||
|---|---|---|---|---|---|
| Analysis of Grit Chamber Sludge | |||||
| Velocity Feet per Second | Specific Gravity | Per Cent Moisture | Calculated to Dry Weight, Per Cent | ||
| Nitrogen | Fixed Matter | Miscellaneous | |||
| 1.0 | 1.5 | 45 | 20 | 78 | 2 |
236. Dimensions of Grit Chambers.—The quantity of sewage to be treated and the amount and character of the settling solids which it contains should be determined by measurement and analysis, and the amount of settling solids to be removed should be determined by a study of the desired conditions of disposal, in order that a grit chamber that will accomplish the desired results may be designed. The period of retention and the velocity of flow are the controlling features in the successful operation of any grit chamber. These should be determined by experiment or as the result of experience. Where neither are available, Hazen’s method can be followed or a decision made based on a study of other grit chambers. In general, the period of retention in grit chambers is from 30 to 90 seconds, and the velocity of flow is about one foot per second.
After having determined the quantity of sewage to be treated, the quantity of grit to be stored between cleanings, the period of retention, the arrangement of the chambers, and the velocity of flow to be used, the overall dimensions of the chambers are computed. The capacity of the chamber is fixed as the sum of the quantity of sewage to be treated during the period of retention and the required storage capacity for grit accumulated between cleanings. The length of the chamber is fixed as the product of the velocity of flow and the period of retention. The cross-sectional area of the portion of the chamber devoted to sedimentation is fixed as the quotient of the quantity of flow of sewage per unit time and the velocity of flow. Only the relation between the width and depth of the portion devoted to sedimentation and the portion devoted to the storage of grit remain to be determined. These should be so designed as to give the greatest economy of construction commensurate with the required results. They will be affected by the local conditions such as topography, available space, difficulties of excavation, etc. Common depths in use lie between 8 and 12 feet, although wide variations can be found. A study of the proportions of existing grit chambers will be of assistance in the design of other basins.
237. Existing Grit Chambers.—The details of some typical grit chambers are shown in Figs. 155 and 156. The grit chamber at the foot of 58th Street, in Cleveland, Ohio, is shown in Fig. 155. The special feature of this structure is the shape of the sedimentation basin, the bottom of which is formed by sloping steel plates forming a 6–inch longitudinal slot above the grit storage chamber. Flows between 8,000,000 and 16,000,000 gallons per day are controlled by the outlet weir so that the velocity of flow remains at one foot per second. This is accomplished by increasing the depth of flow in the same ratio as the increase in the rate of flow. The bottoms of the two chambers differ, one having a special hopper for grit and the other a flat bottom. This is due to the method of cleaning the chambers, it being necessary in the one with a flat bottom to shut off the flow when removing the grit while in the one with the hopper bottom it is hoped to remove the grit by the use of sand ejectors without stopping the sewage flow. The details of the chamber at Hamilton, Ontario, are shown in Fig. 156. In studying these drawings the following features should be noted: 1st, the smooth curves in the channel to prevent eddies, undue deposition of organic matter, and difficulties in cleaning; 2nd, the hopper in the upper end of the grit storage chamber and the slope of the bottom of at least 1:20; and 3rd, the simplicity of the inlet and outlet devices which may be either stop planks or cast-iron sluice gates.
Fig. 155.—Grit Chamber at Cleveland, Ohio.
Eng. Record, Vol. 73, 1916, p. 409.
Fig. 156.—Grit Chamber at Hamilton, Ontario.
Eng. News, Vol. 73, 1915, p. 425.
The drawings shown are merely representative of some satisfactory types. The number and variety of grit chambers in existence is great. In designing grit chambers consideration must be given to the method of cleaning. They are ordinarily cleaned by such methods as have been described for the cleaning of catch-basins in Chapter XII. Continuous bucket scrapers similar to excavating machines are sometimes used for the cleaning of large grit chambers. The period between cleanings is variable. The design should be such as not to require more frequent cleanings than twice a month under the worst conditions. The fluctuations in quality and quantity of grit will vary the period between cleanings.
238. Number of Grit Chambers.—The period of retention in grit chambers is so short and the velocity of flow so near the maximum and minimum limitations that the wide fluctuations in the rate of discharge in storm and combined sewers necessitates the construction of a number of chambers which should be operated in parallel in order to maintain the velocity between the proper limits. Unless arrangements are made permitting the cleaning of grit chambers during operation, more than one grit chamber should be installed in order that when one is being cleaned the others may be in operation. The number of grit chambers must be determined by the desired conditions of operation and the cost of construction. The larger the number of basins the more nearly the flow in any one basin can be maintained constant, but the more expensive the construction. The increase in velocity of flow with increasing quantity is dependent on the outlet arrangements. In a shallow chamber with vertical sides and a standard sharp-crested rectangular weir at the outlet the velocity will vary approximately as the cube root of the rate of flow. Similarly if the outlet is a V notch the velocity will vary as the fifth root of the rate of flow. In all cases the deeper the basin the more nearly the velocity varies directly as the rate of flow. The outlet weir can be arranged as at Cleveland, so that the velocity remains constant for all rates of flow within certain limits. It is seldom that more than three grit chambers are necessary to care for the fluctuations in flow.
239. Quantity and Characteristics of Sludge from Plain Sedimentation.—The sludge removed from plain sedimentation basins is slimy, offensive, not easily dried, and is highly putrescible and odoriferous. It contains about 90 per cent moisture and has a specific gravity from 1.01 to 1.05. The amount removed varies between 2 and 5 cubic yards per million gallons of sewage. The percentage of suspended matter removed varies between 20 and 60. The total amount removed and the percentage removal depend on the character of the sewage, the type of basin, and the period of detention.
240. Dimensions of Sedimentation Basins.—The dimensions of a sedimentation basin are determined by a method similar to the one given for the determination of the dimensions of a grit chamber in Art. 236. The capacity of the basin is first fixed upon to give the required period of sedimentation and sludge storage capacity. The length of the basin is the product of the velocity and the period of retention. The length, width, and depth of the basin are normally fixed by considerations of economy and the limitations of the local conditions, such as available area, topography, foundations, etc., and examples of good practice. A study of basins in use shows the relation between length and width to vary normally between 2:1 and 4:1. Widths greater than 30 to 50 feet are undesirable because of the danger of cross currents and back eddies which will reduce the efficiency of the sedimentation. Depths used in practice vary too widely to act as guides for any particular design. Theoretically the shallower the basin the better the result. Tanks abroad have been built as shallow as 3 feet and some in this country as deep as 16 feet. The economical dimensions can be determined by trial or by calculus. They will serve as a guide in the adoption of the final dimensions.
The method to be pursued in determining the economical dimensions of any engineering structure are:
I. Express the total cost of the structure in terms of as few variables as possible.
II. Express all of the variables in terms of any one and rewrite the expression for the total cost in terms of this one variable.
III. Equate the first derivative of the expression with regard to this variable to zero and solve for the variable. The result will be the economical value of the variable. The values of the other variables can be computed from the relations already expressed.
Fig. 157.—Diagram for the Computation of Economical Basin Dimensions.
For example, let it be desired to determine the dimensions of two continuous-flow sedimentation basins as shown in Fig. 157, in which the period of retention in each is to be 2 hours, the velocity of flow is not to exceed one foot per second, and the sludge accumulated will be 3 cubic yards per million gallons of sewage treated. The quantity of sewage to be treated is 18,000,000 gallons per day. The shortest time between cleanings will be 2 weeks.
The capacity of each basin must be 2
24 of 18,000,000 gallons, or 200,000 cubic feet in order to allow a period of retention of 2 hours. To this volume should be added sufficient capacity to allow for the 2 weeks of sludge storage between cleanings. When a basin is being cleaned the load must be put on the remaining basins. Then if Q represents the rate of accumulation of sludge per day, n represents the number of days between cleanings, m represents the number of basins, and S the sludge capacity of one basin, then
S = Q(n − 1)
m + Q
m − 1
The sludge storage capacity for the example given will be approximately 11,000 cubic feet.
In expressing the total cost of the basins let
h = the depth in feet.
l = the length in feet.
b = the width in feet.
| The cost of land, floor, etc., per square foot | = p dollars. |
| The cost of wall per foot length | = qh2 dollars. |
| The cost of pipes, valves and appurtenances | = P dollars. |
| Then the total cost C = (3l + 4b)qh2 + 2plb + P. | |
It is now necessary to express the three variables b, l, and h, in terms of one of them. From the relation Q = 2blh it is possible to rewrite the expression for the total cost as:
C = (3Q
2bh + 4b)qh2 + pQ
h + P.
C = (3l + 2Q
lh)qh2 + pQ
h + P.
Holding h constant and differentiating with regard to b in the first expression and with regard to l in the second expression, equating to zero and solving we get:
b = √3Q
8h and l = √2Q
3h.
The economical relation between b and l is therefore
b = 0.75l
regardless of the value of h.
Substituting these values of l and b in the original expression for the total cost, it becomes
C = (3√2Q
3h + 4√3Q
8h)qh2 + pQ
h + P.
Differentiating with regard to h, equating to zero, and solving
h = 0.45(pQ½
q)⅔.
In the example given if q = 0.2 and p = 1.0 then
h = 11.6 feet, b = 120 feet and l = 160 feet.
Since these are reasonable dimensions and in accord with good practice they should be used, unless other conditions are unsuitable or the velocity of flow is too great. A width of channel of 120 feet as compared to a length of 160 feet is conducive to a poor distribution of velocity across the basin. A ratio of width to length of about 1:4 is desirable. In this case, by the use of three baffles parallel to the length of the basin, thus dividing it into channels 40 feet wide and 11.6 feet deep, the ratio of width to length is changed to 1:4 and the velocity will be increased only to 0.06 foot per second or 3.6 feet per minute, which is a reasonable velocity. It could be reduced by increasing the spacing of the baffles or the depth of the chamber.
Complicated baffling is undesirable. Two or three overflow baffles may be used to permit quiescent sedimentation in the space thus formed, and hanging baffles may be placed before the inlet and outlet to break up surface currents, or to prevent the movement of scum. The hanging baffles should not extend more than 12 to 18 inches below the water surface. The inlet and outlet are sometimes arranged to permit the reversal of flow, and the connecting channels between basins to allow the operation of any number of basins in series or in parallel, although such arrangements are more important in water purification. Sewage should enter and leave at the top of the basin.
Fig. 158.—Section through a Dortmund Tank.
Depth 20 to 30 feet.
Cleaning is facilitated by the location of a central gutter in the bottom of the basin with the slope of the bottom of the basin towards the gutter from 1:25 to 1:80 or steeper. A pipe, 2 inches or larger in diameter, containing water under pressure with connections for hose placed at frequent intervals is a useful adjunct in flushing the sludge from the sedimentation basins. For equal capacity, deep vertical flow tanks are more expensive and difficult to construct than the shallower rectangular type. Deep tanks are advantageous, however, in that sludge can sometimes be removed by gravity or by pumping without stopping the operation of the tank. They will also operate successfully with shorter periods of detention and higher velocities. The upward velocity should not be greater than the velocity of sedimentation of the smallest particle to be removed. The efficiency of sedimentation in them will be increased by the sedimentation of the larger particles which drag some of the smaller particles down with them. The Dortmund tank shown in Fig. 158 is an example of this type.
Ordinarily it is not necessary to roof sedimentation basins as the odors created are not strong, and difficulties with ice are seldom serious.